1. Field of the Invention
The invention relates generally to acoustic (sonic or ultrasonic) logging.
2. Background Art
In a typical oil or gas well drilling process, a string of casing, typically made of steel, is lowered into the well bore after the drill pipe is removed. Drilling or logging fluid, such as water-based mud (WMB) or oil-based mud (OBM), is used in the well bore to compensate the formation pressure. A fill material (typically cement) is then pumped into the annulus between the casing and the well wall, and replaces the mud and forms a sheath (or a cement bond as it is often called) serving the functions of isolating formation layers and protecting the casing.
The evaluation of the cement bond is important for determining whether the bond functions properly to prevent liquids (such as water, oil, or mud) from migrating from one formation layer to another. Such an evaluation is typically done during cement bond logging, using sonic or ultrasonic transmitters and sensors. During acoustic logging, acoustic pulses are emitted from the transmitters in a sonde. These pulses pass through the fluids inside the casing, and are partially reflected from the fluid/steel interface. Part of the pulses propagate further and are partially reflected at the steel/cement interface and the cement/formation interface. The reflected signals are recorded by the sensors and analyzed.
Cement bond logging using acoustic sensors depends on the impedance mismatching between steel casing and fluids as compared to casing and cement. To a rough approximation the impedance of a material 1 (Z1) can be expressed as:Z1=ρ01C1  Eq. (1)where ρ01 is the static density of the material 1, C1 is the speed of sound in the material 1. The transmitted and reflected amplitude of acoustic waves at the interface between material 1 and material 2 of different impedances is given by:
                                                        A              i                        -                          A              r                                =                                                                      Z                  1                                ⁢                                                                  ⁢                sec                ⁢                                                                  ⁢                                  Θ                  1                                                                              Z                  1                                ⁢                                                                  ⁢                sec                ⁢                                                                  ⁢                                  Θ                  2                                                      ⁢                          A              t                                      ;                            Eq        .                                  ⁢                  (          2          )                    where Ai is the amplitude of the incident wave, Ar is the amplitude of the reflected wave, At is the amplitude of the transmitted wave, Θ1 is the angle of propagation in material 1 and Θ2 is the angle of propagation in material 2, measured from an axis perpendicular to the interface. When the impedance of a material is non-isotropic, Z has a tensor form. For exemplary purposes we do not use the tensor description of Z. There are also constant factors that normalize Eq. (2) to yield fractional results which have been omitted. The simple form of Eq. (2) is used throughout the application to illustrate the physical principles involved.